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Solitonic solutions for a variable-coefficient variant Boussinesq system in the long gravity waves |
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| Authors: | De-Xin Meng Xiao-Ling Gai Xin Yu Ming-Zhen Wang |
| Institution: | a Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China b State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China c School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China |
| Abstract: | Variable-coefficient variant Boussinesq (VCVB) system is able to describe the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth. In this paper, with symbolic computation, a Lax pair associated with the VCVB system under some constraints for variable coefficients is derived, and based on the Lax pair, two sorts of basic Darboux transformations are presented. By applying the Darboux transformations, some solitonic solutions are obtained, with the relevant constraints given in the text. In addition, the VCVB system is transformed to a variable-coefficient Broer-Kaup system. Solitonic solutions and procedure of getting them could be helpful to solve the nonlinear and dispersive problems in fluid dynamics. |
| Keywords: | Lax pair Variable-coefficient variant Boussinesq system Nonlinear wave Fluid dynamics Solitonic solution Darboux transformation |
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